Henry Bannerman Morrison (20 September 1850 — 10 November 1913) was a Scottish-born New Zealand cricketer who played for Otago. He was born in Glasgow and died in Burgess Hill, Sussex.
A batsman and medium-pace bowler, Henry Morrison played for Southland against the English touring team in March 1877, winning the prize for the best fieldsman in the match. A year later, against the Australian touring team, he took 6 for 87. He later made a single first-class appearance for Otago, during the 1880–81 season, against Canterbury. From the lower-middle order, he scored 17 runs in the first innings in which he batted, and a duck in the second, as Otago lost the match by an innings.